a history of science-1-第40节

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correct　methods　of　measurement。　Let　it　be　particularly　observed；　however；　that　all　the　conclusions　of　Aristarchus　are　stated　in　relative　terms。　He　nowhere　attempts　to　estimate　the　precise　size　of　the　earth；　of　the　moon；　or　of　the　sun；　or　the　actual　distance　of　one　of　these　bodies　from　another。　The　obvious　reason　for　this　is　that　no　data　were　at　hand　from　which　to　make　such　precise　measurements。　Had　Aristarchus　known　the　size　of　any　one　of　the　bodies　in　question；　he　might　readily；　of　course；　have　determined　the　size　of　the　others　by　the　mere　application　of　his　relative　scale；　but　he　had　no　means　of　determining　the　size　of　the　earth；　and　to　this　extent　his　system　of　measurements　remained　imperfect。　Where　Aristarchus　halted；　however；　another　worker　of　the　same　period　took　the　task　in　hand　and　by　an　altogether　wonderful　measurement　determined　the　size　of　the　earth；　and　thus　brought　the　scientific　theories　of　cosmology　to　their　climax。　This　worthy　supplementor　of　the　work　of　Aristarchus　was　Eratosthenes　of　Alexandria。

ERATOSTHENES；　〃THE　SURVEYOR　OF　THE　WORLD〃　An　altogether　remarkable　man　was　this　native　of　Cyrene；　who　came　to　Alexandria　from　Athens　to　be　the　chief　librarian　of　Ptolemy　Euergetes。　He　was　not　merely　an　astronomer　and　a　geographer；　but　a　poet　and　grammarian　as　well。　His　contemporaries　jestingly　called　him　Beta　the　Second；　because　he　was　said　through　the　universality　of　his　attainments　to　be　〃a　second　Plato〃　in　philosophy；　〃a　second　Thales〃　in　astronomy；　and　so　on　throughout　the　list。　He　was　also　called　the　〃surveyor　of　the　world；〃　in　recognition　of　his　services　to　geography。　Hipparchus　said　of　him；　perhaps　half　jestingly；　that　he　had　studied　astronomy　as　a　geographer　and　geography　as　an　astronomer。　It　is　not　quite　clear　whether　the　epigram　was　meant　as　compliment　or　as　criticism。　Similar　phrases　have　been　turned　against　men　of　versatile　talent　in　every　age。　Be　that　as　it　may；　Eratosthenes　passed　into　history　as　the　father　of　scientific　geography　and　of　scientific　chronology；　as　the　astronomer　who　first　measured　the　obliquity　of　the　ecliptic；　and　as　the　inventive　genius　who　performed　the　astounding　feat　of　measuring　the　size　of　the　globe　on　which　we　live　at　a　time　when　only　a　relatively　small　portion　of　that　globe's　surface　was　known　to　civilized　man。　It　is　no　discredit　to　approach　astronomy　as　a　geographer　and　geography　as　an　astronomer　if　the　results　are　such　as　these。　What　Eratosthenes　really　did　was　to　approach　both　astronomy　and　geography　from　two　seemingly　divergent　points　of　attacknamely；　from　the　stand…point　of　the　geometer　and　also　from　that　of　the　poet。　Perhaps　no　man　in　any　age　has　brought　a　better　combination　of　observing　and　imaginative　faculties　to　the　aid　of　science。　Nearly　all　the　discoveries　of　Eratosthenes　are　associated　with　observations　of　the　shadows　cast　by　the　sun。　We　have　seen　that；　in　the　study　of　the　heavenly　bodies；　much　depends　on　the　measurement　of　angles。　Now　the　easiest　way　in　which　angles　can　be　measured；　when　solar　angles　are　in　question；　is　to　pay　attention；　not　to　the　sun　itself；　but　to　the　shadow　that　it　casts。　We　saw　that　Thales　made　some　remarkable　measurements　with　the　aid　of　shadows；　and　we　have　more　than　once　referred　to　the　gnomon；　which　is　the　most　primitive；　but　which　long　remained　the　most　important；　of　astronomical　instruments。　It　is　believed　that　Eratosthenes　invented　an　important　modification　of　the　gnomon　which　was　elaborated　afterwards　by　Hipparchus　and　called　an　armillary　sphere。　This　consists　essentially　of　a　small　gnomon；　or　perpendicular　post；　attached　to　a　plane　representing　the　earth's　equator　and　a　hemisphere　in　imitation　of　the　earth's　surface。　With　the　aid　of　this；　the　shadow　cast　by　the　sun　could　be　very　accurately　measured。　It　involves　no　new　principle。　Every　perpendicular　post　or　object　of　any　kind　placed　in　the　sunlight　casts　a　shadow　from　which　the　angles　now　in　question　could　be　roughly　measured。　The　province　of　the　armillary　sphere　was　to　make　these　measurements　extremely　accurate。　With　the　aid　of　this　implement；　Eratosthenes　carefully　noted　the　longest　and　the　shortest　shadows　cast　by　the　gnomonthat　is　to　say；　the　shadows　cast　on　the　days　of　the　solstices。　He　found　that　the　distance　between　the　tropics　thus　measured　represented　47　degrees　42'　39〃　of　arc。　One…half　of　this；　or　23　degrees　5；'　19。5〃；　represented　the　obliquity　of　the　eclipticthat　is　to　say；　the　angle　by　which　the　earth's　axis　dipped　from　the　perpendicular　with　reference　to　its　orbit。　This　was　a　most　important　observation；　and　because　of　its　accuracy　it　has　served　modern　astronomers　well　for　comparison　in　measuring　the　trifling　change　due　to　our　earth's　slow；　swinging　wobble。　For　the　earth；　be　it　understood；　like　a　great　top　spinning　through　space；　holds　its　position　with　relative　but　not　quite　absolute　fixity。　It　must　not　be　supposed；　however；　that　the　experiment　in　question　was　quite　new　with　Eratosthenes。　His　merit　consists　rather　in　the　accuracy　with　which　he　made　his　observation　than　in　the　novelty　of　the　conception；　for　it　is　recorded　that　Eudoxus；　a　full　century　earlier；　had　remarked　the　obliquity　of　the　ecliptic。　That　observer　had　said　that　the　obliquity　corresponded　to　the　side　of　a　pentadecagon；　or　fifteen…sided　figure；　which　is　equivalent　in　modern　phraseology　to　twenty…　four　degrees　of　arc。　But　so　little　is　known　regarding　the　way　in　which　Eudoxus　reached　his　estimate　that　the　measurement　of　Eratosthenes　is　usually　spoken　of　as　if　it　were　the　first　effort　of　the　kind。　Much　more　striking；　at　least　in　its　appeal　to　the　popular　imagination；　was　that　other　great　feat　which　Eratosthenes　performed　with　the　aid　of　his　perfected　gnomonthe　measurement　of　the　earth　itself。　When　we　reflect　that　at　this　period　the　portion　of　the　earth　open　to　observation　extended　only　from　the　Straits　of　Gibraltar　on　the　west　to　India　on　the　east；　and　from　the　North　Sea　to　Upper　Egypt；　it　certainly　seems　enigmaticalat　first　thought　almost　miraculousthat　an　observer　should　have　been　able　to　measure　the　entire　globe。　That　he　should　have　accomplished　this　through　observation　of　nothing　more　than　a　tiny　bit　of　Egyptian　territory　and　a　glimpse　of　the　sun's　shadow　makes　it　seem　but　the　more　wonderful。　Yet　the　method　of　Eratosthenes；　like　many　another　enigma；　seems　simple　enough　once　it　is　explained。　It　required　but　the　application　of　a　very　elementary　knowledge　of　the　geometry　of　circles；　combined　with　the　use　of　a　fact　or　two　from　local　geographywhich　detracts　nothing　from　the　genius　of　the　man　who　could　reason　from　such　simple　premises　to　so　wonderful　a　conclusion。　Stated　in　a　few　words；　the　experiment　of　Eratosthenes　was　this。　His　geographical　studies　had　taught　him　that　the　town　of　Syene　lay　directly　south　of　Alexandria；　or；　as　we　should　say；　on　the　same　meridian　of　latitude。　He　had　learned；　further；　that　Syene　lay　directly　under　the　tropic；　since　it　was　reported　that　at　noon　on　the　day　of　the　summer　solstice　the　gnomon　there　cast　no　shadow；　while　a　deep　well　was　illumined　to　the　bottom　by　the　sun。　A　third　item　of　knowledge；　supplied　by　the　surveyors　of　Ptolemy；　made　the　distance　between　Syene　and　Alexandria　five　thousand　stadia。　These；　then；　were　the　preliminary　data　required　by　Eratosthenes。　Their　significance　consists　in　the　fact　that　here　is　a　measured　bit　of　the　earth's　arc　five　thousand　stadia　in　length。　If　we　could　find　out　what　angle　that　bit　of　arc　subtends；　a　mere　matter　of　multiplication　would　give　us　the　size　of　the　earth。　But　how　determine　this　all…important　number？　The　answer　came　through　reflection　on　the　relations　of　concentric　circles。　If　you　draw　any　number　of　circles；　of　whatever　size；　about　a　given　centre；　a　pair　of　radii　drawn　from　that　centre　will　cut　arcs　of　the　same　relative　size　from　all　the　circles。　One　circle　may　be　so　small　that　the　actual　arc　subtended　by　the　radii　in　a　given　case　may　be　but　an　inch　in　length；　while　another　circle　is　so　large　that　its　corresponding　are　is　measured　in　millions　of　miles；　but　in　each　case　the　same　number　of　so…called　degrees　will　represent　the　relation　of　each　arc　to　its　circumference。　Now；　Eratosthenes　knew；　as　just　stated；　that　the　sun；　when　on　the　meridian　on　the　day　of　the　summer　solstice；　was　directly　over　the　town　of　Syene。　This　meant　that　at　that　moment　a　radius　of　the　earth　projected　from　Syene　would　point　directly　towards　the　sun。　Meanwhile；　of　course；　the　zenith　would　represent　the　projection　of　the　radius　of　the　earth　passing　through　Alexandria。　All　that　was　required；　then；　was　to　measure；　at　Alexandria；　the　angular　distance　of　the　sun　from　the　zenith　at　noon　on　the　day　of　the　solstice　to　secure　an　approximate　measurement　of　the　arc　of　the　sun's　circumference；　corresponding　to　the　arc　of　the　earth's　surface　represented　by　the　measured　distance　between　Alexandria　and　Syene。　The　reader　will　observe　that　the　measurement　could　not　be　absolutely　accurate；　because　it　is　made　from　the　surface　of　the　earth；　and　not　from　the　earth's　centre；　but　the　size　of　the　earth　is　so　insignificant　in　comparison　with　the　distance　of　the　sun　that　this　slight　discrepancy　could　be　disregarded。　The　way　in　which　Eratosthenes　measured　this　angle　was　very　simple。　He　merely　measured　the　angle　of　the　shadow　which　his　perpendicular　gnomon　at　Alexandria　cast　at　mid…day　on　the　day　of